V起 lifts the object off a surface and the object follows it (拿起筆); V起來1 traces the full upward arc to standing or aloft and can stand alone with no object (站起來). 起 is the lift; 起來 is the whole rise.
趨向補語 is the family of path tags (出 out, 進 in, 下 down); 起 is the up-off-a-surface member, the start of a rise rather than a full directional sweep.
✗ 他起拿筆。 → ✓ 他拿起筆。 (起 follows the verb, never leads it.)
✗ 他拿筆起。 → ✓ 他拿起筆。 (起 sits right behind the verb; the object comes after 起.)
✗ 他放起筆。(for setting it down) → ✓ 他放下筆。 (起 only lifts up off a surface; a downward path takes 下.)
English 'pick up the pen' lets 'up' float to the end after the object; Chinese fixes 起 right behind the verb and the object follows it (拿起筆), never 拿筆起.